Question

A student scored 83 and 91 on their first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give them an average between 85 and 90, inclusive

Answer 1

to find the mean of a data set, we follow the following formula

Mean = sum of values in data set ÷ number of values in data set

We have three values in given data set: 83, 91, and an unknown value
`x`

We want to work out a range of possible value of
`x` such as the mean is in between 85 and 90 inclusive

We first set the inequality

`85 \leq Mean \leq 90`

`85 \leq (83+91+x)/(3) \leq 90`

`85 \leq (174+x)/(3) \leq 90`, multiply each term by 3

`255 \leq 174+x \leq 270`, subtract 174 from each term

`81 \leq x \leq 96`

So the possible values of x are in between 81 and 96 inclusive